Highest Common Factor of 187, 660, 265 using Euclid's algorithm
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 187, 660, 265 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 187, 660, 265 is 1 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.
Consider we have numbers 187, 660, 265 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b
Highest common factor (HCF) of 187, 660, 265 is 1.
HCF(187, 660, 265) = 1
HCF of 187, 660, 265 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 187, 660, 265 is 1.
Highest Common Factor of 187,660,265 is 1
Step 1: Since 660 > 187, we apply the division lemma to 660 and 187, to get
660 = 187 x 3 + 99
Step 2: Since the reminder 187 ≠ 0, we apply division lemma to 99 and 187, to get
187 = 99 x 1 + 88
Step 3: We consider the new divisor 99 and the new remainder 88, and apply the division lemma to get
99 = 88 x 1 + 11
We consider the new divisor 88 and the new remainder 11, and apply the division lemma to get
88 = 11 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 11, the HCF of 187 and 660 is 11
Notice that 11 = HCF(88,11) = HCF(99,88) = HCF(187,99) = HCF(660,187) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 265 > 11, we apply the division lemma to 265 and 11, to get
265 = 11 x 24 + 1
Step 2: Since the reminder 11 ≠ 0, we apply division lemma to 1 and 11, to get
11 = 1 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 11 and 265 is 1
Notice that 1 = HCF(11,1) = HCF(265,11) .
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Frequently Asked Questions on HCF of 187, 660, 265 using Euclid's Algorithm
1. What is the Euclid division algorithm?
Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.
2. what is the HCF of 187, 660, 265?
Answer: HCF of 187, 660, 265 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 187, 660, 265 using Euclid's Algorithm?
Answer: For arbitrary numbers 187, 660, 265 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.